Sequences of Problems, Matrices, and Solutions
De Sturler, Eric
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In a wide range of applications, we deal with long sequences of slowly changing matrices or large collections of related matrices and corresponding linear algebra problems. Such applications range from the optimal design of structures to acoustics and other parameterized systems, to inverse and parameter estimation problems in tomography and systems biology, to parameterization problems in computer graphics, and to the electronic structure of condensed matter. In many cases, we can reduce the total runtime significantly by taking into account how the problem changes and recycling judiciously selected results from previous computations. In this presentation, I will focus on solving linear systems, which is often the basis of other algorithms. I will introduce the basics of linear solvers and discuss relevant theory for the fast solution of sequences or collections of linear systems. I will demonstrate the results on several applications and discuss future research directions.